Issued 31 October 2023: the next three dekads

Subseasonal rainfall forecasts for Indonesia from one day’s GEFSv12 run, one to three dekads ahead

Case 05 · Subseasonal · Dekad rainfall · Full Indonesia

At the end of every dekad (dasarian: days 1-10, 11-20 and 21 to the end of a month) a forecaster can ask how much rain will fall in each of the next three dekads. Dekads are the unit BMKG uses for its rainfall early warnings. This case takes the GEFSv12 run started at 00 UTC on 31 October 2023 and forecasts the three dekads of November: 1-10, 11-20 and 21-30 November. It is calibrated with CCA and PCR through CPT against the CHIRPS v3.0 dekad product at its native 0.05° grid, 61,190 pixels over Indonesia.

It is the same moment as the monthly and seasonal cases, issued the day before them. All numbers come from the executed notebook.

Hover, tap or use the arrow keys on any map or chart to read values; each view can be downloaded as it is set. Maps load when you choose them, one small file per map.

NoteThe short result
  • The forecast of 31 October leaned dry, and November started dry. The first two dekads brought 60 and 68 mm over Indonesia against normals of 89 and 98 mm. The forecast (CCA) was 67 and 80 mm: drier than normal, not as dry as observed. The third dekad was close to normal (94 mm) and was forecast at 89 mm.
  • For dekads +1 and +2 the most likely category matched the observed one over 64% to 65% of the area, the same as always saying “below normal”; for dekad +3 it was 35% against 38%.
  • How far to trust each lead, from all October-December dekads of 2000-2018: the area-mean CCA correlation is 0.35 one dekad ahead, 0.31 two dekads ahead and 0.17 three dekads ahead. The raw GEFSv12 correlation is higher at every lead (0.42, 0.32 and 0.20).

The forecast issued on 31 October 2023

A forecast is issued on the last day of a dekad, from the GEFSv12 run started at 00 UTC that day. Dekad +1 starts the next day, dekad +2 eleven or twelve days later, dekad +3 twenty-one or twenty-two days later; the third ends by model day 31, inside the model’s 35 days. GEFSv12 runs every day, so every 2023 issue date uses its own run. The menus start at this forecast and add the three later issue dates, up to 30 November 2023, the last whose three leads all fall in October-December, the period forecast and verified here.

Each map is one lead against its own target, dekad +1 at the top.

CCA forecast issued 31 October 2023, area-weighted over Indonesia. Source: issued-2023-10-31.csv, which also has PCR.
Lead Target Forecast (mm) Observed (mm) 2000-2018 mean (mm) Observed below / near / above normal (% of area) Hit rate (%) Reference (%)
Dekad +1 1-10 Nov 67.2 60.3 89.2 64.4 / 31.1 / 4.5 64.9 64.4
Dekad +2 11-20 Nov 79.5 67.9 98.3 64.4 / 27.6 / 8.0 64.1 64.4
Dekad +3 21-30 Nov 89.3 94.2 98.9 36.0 / 38.2 / 25.9 34.7 38.2
  • Amounts. The first two dekads of November were dry, 60 and 68 mm against normals of 89 and 98 mm. The forecast went the same way but stopped short: 67 and 80 mm. The third dekad was near normal (94 mm against 99 mm) and was forecast at 89 mm.
  • Categories. For dekads +1 and +2 the forecast made below normal the most likely category over 97% to 98% of the area, and below normal was observed over 64% of it. The hit rate (64.9% and 64.1%) equalled the reference, always forecasting the category that turned out most common, chosen with hindsight. For dekad +3, a mixed dekad, the forecast still favoured below normal over 81% of the area; its hit rate was 34.7% against 38.2%.

One issue date is one outcome per lead. The next sections show how well each lead does on average.

How far each lead can be trusted

The calibration of each lead is trained and scored on every October-December dekad of 2000-2018, 171 per lead. GEFSv12’s hindcasts start only on Wednesdays, so each training sample uses the one Wednesday whose start falls in a 7-day window around the real-time offset: 1-7 days before the target for dekad +1, 8-14 for dekad +2, 18-24 for dekad +3. Dekad +1 is the one compromise: its training starts are 1-7 days before the target, its real-time start one day before, so training is on average slightly harder than real use.

CCA (3 predictor and 3 predictand EOFs, 2 CCA modes) and PCR (3 predictor EOFs) are fitted through cptcore, the layer PyCPT’s evaluate_models calls, with cross-validation leaving out 17 dekads at a time (the held-out dekad and 8 on each side, about a season). At 0.05° one fit took 32 to 38 minutes for CCA and 13 to 14 minutes for PCR; the six fits ran in parallel. For every fit, CPT’s correlation map equals the correlation recomputed from its own cross-validated hindcasts to within 0.000001.

Pearson correlation is 0 for no linear relationship; 2AFC is the chance that the forecast ranks two different dekads in the observed order, 50% for no skill (Mason and Weigel 2009).

Area-weighted means over 61,190 pixels, 171 dekads of 2000-2018. Source: skill-by-lead.csv.
Lead CCA Pearson PCR Pearson Raw GEFS Pearson CCA 2AFC (%) PCR 2AFC (%)
Dekad +1 0.35 0.34 0.42 62.7 62.5
Dekad +2 0.31 0.31 0.32 60.8 60.9
Dekad +3 0.17 0.17 0.20 57.0 56.8
  1. Skill falls with each dekad of lead, most between dekads +2 and +3: CCA’s mean correlation drops by 0.04 and then by 0.14.
  2. Calibration does not beat the raw model. GEFSv12’s own anomaly correlates better at every lead, by 0.07 one dekad ahead and 0.01 to 0.03 after that. The calibrated scores pay a cross-validation cost (Barnston and van den Dool 1993) and see the model only through 3 EOF patterns; neither effect was measured here.
  3. CCA and PCR are nearly identical, within 0.01 at every lead.

Where the skill is, pixel by pixel

The whole season: October-December 2023

Every dekad of October-December 2023 is forecast at every lead, so the scores below also use the issue dates of September and December whose forecasts reach into the season only in part: eleven issue dates in all, from 10 September to 20 December. Over the nine dekads of each lead, scored over every pixel and dekad (area-weighted):

Nine dekads of October-December 2023, area-weighted. Observed: below normal 53.8%, near normal 31.3%, above normal 14.9% of area × dekads. Source: ond-2023-dekad-forecasts.csv.
Lead Method Hit rate (%) Reference (%) RPSS 2023 RMSE 2023 (mm) Mean forecast (mm) Observed mean (mm)
Dekad +1 CCA 52.7 53.8 0.16 37.4 82.5 71.9
Dekad +1 PCR 52.4 53.8 0.16 37.5 82.4 71.9
Dekad +2 CCA 45.2 53.8 0.08 40.2 85.9 71.9
Dekad +2 PCR 45.0 53.8 0.07 40.6 85.7 71.9
Dekad +3 CCA 50.6 53.8 0.09 39.5 84.7 71.9
Dekad +3 PCR 49.3 53.8 0.09 39.7 84.4 71.9
  • The area-mean total was below the 2000-2018 average in 8 of the 9 dekads; only 1-10 December was slightly above. The forecasts followed the dry spell but sat between the observations and the average: 82.4 to 85.9 mm per dekad against an observed 71.9 mm.
  • Hit rate: always forecasting “below normal” would have scored 53.8%. No lead did better over the season; one dekad ahead came closest (52.7% for CCA).
  • RPSS 2023, against climatological odds with the ranked probability score (Epstein 1969), was positive at every lead. For nine dekads of one season this rewards leaning the right way in 2023, not skill in general.
  • Totals below zero: where the 2000-2018 mean plus the forecast anomaly fell below zero, the total was set to zero, in 1,686 to 3,196 of the 550,710 CCA pixel-dekads per lead (0.3% to 0.6%).

Observations and anomalies

The predictand is the CHIRPS v3.0 dekad product from the local archive used throughout the tutorial, at its native 0.05° grid; the box is the one of the weekly and pentad cases, so all three subseasonal cases share one pixel grid. The notebook checks every target’s stored time bounds against the design, and that each dekad equals the sum of its two CHIRPS pentads (exactly, for the three dekads checked).

October-December rainfall rises through the season, so model and observations are turned into anomalies from the 2000-2018 mean of the same calendar dekad (and, for the model, the same lead). These means include the year held out in cross-validation; for correlations that makes no difference (it multiplies every anomaly of a dekad by the same factor, 19/18), and its effect inside CPT’s fits was not measured. Each forecast total is the observed mean plus the calibrated anomaly.

Five time scales side by side

The lead-time cases share the observations (CHIRPS v3.0, at 0.05°) and the CCA and PCR mode settings; the cross-validation window is sized to each case’s samples. They differ in model (CFSv2 for months and seasons, GEFSv12 for dekads, weeks and pentads), training years (1991-2020 and 2000-2018), sample size and how lead is counted, so the numbers are not a ranking.

Case Issued Leads CCA correlation, shortest to longest lead Raw model vs calibrated
Monthly 1 Nov 2023 Dec 2023 to May 2024 0.10, then -0.15 to 0.03 raw higher at all 6
Seasonal 1 Nov 2023 DJF 2023-24 to MJJ 2024 0.16, then -0.10 to 0.04 calibrated higher for DJF only
This case 31 Oct 2023 dekads +1 to +3 0.35 to 0.17 raw higher at all 3
Weekly 1 Nov 2023 weeks 1-4, weeks 3-4 0.35 to 0.17 raw higher for weeks 1-2, level from week 3
Pentad 31 Oct 2023 pentads +1 to +6 0.30 to 0.12 raw higher for pentads +1 to +3, level from +4

The monthly and seasonal rows are confounded by the target: each lead there is a different month or season. With one target forecast from earlier starts and the same settings, November keeps a CCA correlation of 0.01 to 0.24 and October-December 0.33 to 0.48.

What this does and does not show

This is one model, one set of fixed settings, 19 training years and one verifying season, with the headline on one issue date. It shows that, for GEFSv12 dekad rainfall over Indonesia in October-December, skill falls with each dekad of lead and that calibration with these settings did not add to the raw model’s correlation. The observations are retrospective CHIRPS v3.0 Final data, not what was available when each forecast was issued, and the 2023 forecasts average 31 GEFSv12 members while the hindcasts have 11.

Files

References

  1. IRI Data Library. SubX EMC GEFSv12_CPC (hindcast and forecast precipitation). https://iridl.ldeo.columbia.edu/SOURCES/.Models/.SubX/.EMC/.GEFSv12_CPC/ Browsing Data Library pages requires signing in (checked 10 November 2026); PyCPT’s data requests in this tutorial succeeded without a key.
  2. Guan, H., Zhu, Y., Sinsky, E., et al. (2022). GEFSv12 reforecast dataset for supporting subseasonal and hydrometeorological applications. Monthly Weather Review, 150(3), 647-665. https://doi.org/10.1175/MWR-D-21-0245.1
  3. BMKG. Peringatan Dini Curah Hujan Dasarian (dekadal rainfall early warnings by regency and city; showed dasarian I November 2026 when checked on 10 November 2026). https://www.bmkg.go.id/iklim/peringatan-dini-hujan-tinggi
  4. Climate Hazards Center, UC Santa Barbara. CHIRPS: Rainfall Estimates from Rain Gauge and Satellite Observations (CHIRPS version 3.0 page). https://www.chc.ucsb.edu/data/chirps3
  5. Funk, C., Peterson, P., Landsfeld, M., et al. (2014). A quasi-global precipitation time series for drought monitoring. U.S. Geological Survey Data Series 832. https://doi.org/10.3133/ds832
  6. Climate Hazards Center. Information about CHIRPS Daily Precipitation (CHIRPS v3.0 daily readme). https://data.chc.ucsb.edu/products/CHIRPS/v3.0/daily/readme.txt
  7. IRI. PyCPT 2.10.4 source: pycpt/src/pycpt/notebook.py (setup, download_data, summarize_available_years, evaluate_models and the plotting functions). Tag pycpt-2.10.4, commit 084bb5c. https://github.com/iri-pycpt/pycpt/blob/084bb5c380c200b5f65f11ba224a965547b91da1/pycpt/src/pycpt/notebook.py
  8. IRI. PyCPT 2.10.4 source: pycpt/src/cptcore/functional/cca.py (canonical_correlation_analysis). Tag pycpt-2.10.4, commit 084bb5c. https://github.com/iri-pycpt/pycpt/blob/084bb5c380c200b5f65f11ba224a965547b91da1/pycpt/src/cptcore/functional/cca.py
  9. IRI. PyCPT 2.10.4 source: pycpt/src/cptextras/redate.py (redate). Tag pycpt-2.10.4, commit 084bb5c. https://github.com/iri-pycpt/pycpt/blob/084bb5c380c200b5f65f11ba224a965547b91da1/pycpt/src/cptextras/redate.py
  10. Mason, S. J., and Weigel, A. P. (2009). A generic forecast verification framework for administrative purposes. Monthly Weather Review, 137(1), 331-349. https://doi.org/10.1175/2008MWR2553.1
  11. Epstein, E. S. (1969). A scoring system for probability forecasts of ranked categories. Journal of Applied Meteorology, 8(6), 985-987. https://doi.org/10.1175/1520-0450(1969)008%3C0985:ASSFPF%3E2.0.CO;2
  12. Barnston, A. G., and van den Dool, H. M. (1993). A degeneracy in cross-validated skill in regression-based forecasts. Journal of Climate, 6(5), 963-977. https://doi.org/10.1175/1520-0442(1993)006%3C0963:ADICVS%3E2.0.CO;2
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